Question

Solve the equations. $$ 2(r+5)-3=3(r-8)+20 $$

   Solve the equations.
$$
2(r+5)-3=3(r-8)+20
$$

Algebra Form and Function

Algebra Form and Function

William G. McCallum,… 1st Edition

Chapter 5, Problem 13

Instant Answer

Solved by Expert Nick Johnson

04/04/2022

Step 1

Step 1: First, distribute the 2 and 3 on the left and right side of the equation respectively: $$ 2(r+5)-3=3(r-8)+20 \Rightarrow 2r+10-3=3r-24+20 $$ Show more…

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Solve the equations. $$ 2(r+5)-3=3(r-8)+20 $$

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Key Concepts

Combining Like Terms

Combining like terms involves consolidating terms in an expression that have the same variable component. By adding or subtracting these terms, the expression is simplified, which is an essential step in solving linear equations.

Linear Equations

A linear equation involves an unknown variable that appears to the first power and can be solved by isolating the variable on one side of the equation. This type of equation forms the basis of algebra and often involves methods like simplifying expressions and performing inverse operations.

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis, converting expressions like a(b + c) into ab + ac. This is a key technique for simplifying equations before combining like terms.

Inverse Operations

Inverse operations are actions performed to undo other operations, such as using subtraction to cancel out addition or division to counteract multiplication. They are crucial in the process of isolating the variable to find its value in an equation.

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